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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeJun 25th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItexWrote rough description. <a href="https://ncatlab.org/nlab/revision/diff/Iwasawa+decomposition/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/Iwasawa+decomposition/2">v2</a>, <a href="https://ncatlab.org/nlab/show/Iwasawa+decomposition">current</a>

   Wrote rough description.

   diff, v2, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 25th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItextouched wording, formatting and hyperlinking <a href="https://ncatlab.org/nlab/revision/diff/Iwasawa+decomposition/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/Iwasawa+decomposition/3">v3</a>, <a href="https://ncatlab.org/nlab/show/Iwasawa+decomposition">current</a>

   touched wording, formatting and hyperlinking

   diff, v3, current

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeJun 25th 2024
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   Author: zskoda
   Format: MarkdownItexIwasawa decomposition is not strictly speaking generalizing the QR-decomposition of matrices as it is not (only) a decomposition of matrices, it has more to the statement. And also less in my understanding, as QR-decomposition is not only for square but for rectangular matrices and no invertibility like in Lie theory is assumed. Thus I would keep a bit more careful wording than saying that it is a generalization.

   Iwasawa decomposition is not strictly speaking generalizing the QR-decomposition of matrices as it is not (only) a decomposition of matrices, it has more to the statement. And also less in my understanding, as QR-decomposition is not only for square but for rectangular matrices and no invertibility like in Lie theory is assumed. Thus I would keep a bit more careful wording than saying that it is a generalization.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 25th 2024
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   Author: Urs
   Format: MarkdownItexBetter to clarify what you mean then.

   Better to clarify what you mean then.

5. • CommentRowNumber5.
   • CommentAuthorzskoda
   • CommentTimeJun 25th 2024
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   Author: zskoda
   Format: MarkdownItexThere is also a quantum group version, discussed e.g. in * [[Branislav Jurčo]], P. Šťovíček, _Quantum dressing orbits on compact groups_, Commun. Math. Physics 152 (1993) 97

   There is also a quantum group version, discussed e.g. in

   • Branislav Jurčo, P. Šťovíček, Quantum dressing orbits on compact groups, Commun. Math. Physics 152 (1993) 97